Sinusoids, phasors, impedance, resonance, RLC transients, power factor, complex power and three-phase basics.
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- General form of a sinusoid in AC circuits
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v(t) = Vm*sin(wt + phi), where Vm is peak voltage, w is angular frequency (rad/s), and phi is phase angle- Relationship between RMS and peak voltage
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Vrms = Vpeak / sqrt(2), approximately 0.707 times the peak value- What is phase angle in a sinusoid?
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The angular offset (in degrees or radians) that determines the sinusoid's starting point at t=0- Relationship between frequency, period, and angular frequency
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T = 1/f and w = 2*pi*f, where T is period, f is frequency in Hz, and w is angular frequency in rad/s- Definition of a phasor
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A complex number representation of a sinusoid, written as V = Vm @ phi or V = Vm*exp(j*phi)- Convert sinusoid v(t) = Vm*sin(wt + phi) to phasor form
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Extract magnitude Vm and phase angle phi, then express as phasor V = Vm @ phi in the frequency domain- Main advantage of using phasors in circuit analysis
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Phasors convert sinusoidal differential equations into algebraic equations, simplifying AC circuit analysis- Definition of impedance
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Z = R + jX, the complex opposition to current flow, with resistance R (real part) and reactance X (imaginary part)- Inductive reactance formula
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XL = w*L = 2*pi*f*L, in ohms, where L is inductance and w is angular frequency- Capacitive reactance formula
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XC = 1/(w*C) = 1/(2*pi*f*C), in ohms, where C is capacitance and w is angular frequency- Impedance of a series RLC circuit
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Z = R + j(wL - 1/(wC)) = R + j(XL - XC), where reactances can be positive or negative- Definition of admittance
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Y = 1/Z, the reciprocal of impedance, measured in siemens (S), inverse of resistance or impedance- Ohm's law in phasor form
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V = Z*I, where V is phasor voltage, Z is impedance, and I is phasor current- Voltage divider formula for impedances
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Vout = Vin * (Z2 / (Z1 + Z2)), generalizing the resistive divider to complex impedances- Condition for resonance in a series RLC circuit
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XL = XC, or wL = 1/(wC), making the imaginary part of impedance zero
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